This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Accumulate[Flatten[Map[ConstantArray[Fibonacci[#],Fibonacci[#-1]]&,Range[15]]]] (* Peter J. C. Moses, May 02 2022 *)
The Zeckendorf representation of 7 = 5 + 2, so a(7) = 2.
a139764 = head . a035517_row -- Reinhard Zumkeller, Mar 10 2013
A000045 := proc(n) combinat[fibonacci](n) ; end: A087172 := proc(n) local a,i ; a := 0 ; for i from 0 do if A000045(i) <= n then a := A000045(i) ; else RETURN(a) ; fi ; od: end: A139764 := proc(n) local nResid,prevF ; nResid := n ; while true do prevF := A087172(nResid) ; if prevF = nResid then RETURN(prevF) ; else nResid := nResid-prevF ; fi ; od: end: seq(A139764(n),n=1..120) ; # R. J. Mathar, May 22 2008
f[n_] := (k = 1; ff = {}; While[(fi = Fibonacci[k]) <= n, AppendTo[ff, fi]; k++]; Drop[ff, 1]); a[n_] := First[ If[n == 0, 0, r = n; s = {}; fr = f[n]; While[r > 0, lf = Last[fr]; If[lf <= r, r = r - lf; PrependTo[s, lf]]; fr = Drop[fr, -1]]; s]]; Table[a[n], {n, 1, 89}] (* Jean-François Alcover, Nov 02 2011 *)
a(n)=my(f);forstep(k=log(n*sqrt(5))\log(1.61803)+2, 2, -1, f=fibonacci(k);if(f<=n,n-=f;if(!n,return(f));k--)) \\ Charles R Greathouse IV, Nov 02 2011
f[n_] := Block[{k = 1}, While[Fibonacci[k] <= n, k++ ]; Return[n - Fibonacci[k - 1]]]; Table[ f[n], {n, 0, 100} ]
a(n) = { my(k=0); while(fibonacci(k) <= n, k++); n-fibonacci(k-1) } \\ Harry J. Smith, Mar 14 2010
h[0] = {1}; h[n_] := Join[h[n - 1], Table[Fibonacci[n + 2], {k, 1, Fibonacci[n]}]]; h[10]
For n = 16 = 2^4, the Zeckendorf representation of 4 is 101, i.e., 4 = Fibonacci(2) + Fibonacci(4) = 1 + 3. Therefore 16 = 2^(1+3) = 2^1 * 2^3, and a(16) = 3.
a(33) = 21*8*3*1 because 33 = 21+8+3+1.
a273156 = product . a035516_row
A273156 := proc(n) local nred,a,f ; if n = 0 then 0; else nred := n ; a := 1 ; while nred > 1 do f := A087172(nred) ; a := a*f ; nred := nred-f ; end do: a ; end if; end proc: # R. J. Mathar, May 17 2016
t = Fibonacci /@ Range@ 21; {0}~Join~Table[Times @@ If[MemberQ[t, n], {n}, Most@ MapAt[# + 1 &, Abs@ Differences@ FixedPointList[# - First@ Reverse@ TakeWhile[t, Function[k, # >= k]] &, n], -1]], {n, 58}] (* Michael De Vlieger, May 17 2016 *)
a[0]=0; a[n_]:=Block[{m=n, p=1, f, k=0}, While[Fibonacci@ ++k <= n]; While[ m>1, f= Fibonacci@ --k; If[ f<=m, m-=f; p*=f]]; p]; Array[a, 80, 0] (* Giovanni Resta, May 17 2016 *)
n = 20 = 13+5+2: a(20) = 5.
The Lucas numbers, beginning with 1, are 1, 3, 4, 7, 11, 18, ..., so that a(5) = 4.
Flatten[Map[ConstantArray[LucasL[#], LucasL[# - 1]] &, Range[15]]] (* Peter J. C. Moses, Apr 30 2022 *)
from itertools import islice def A352717_gen(): # generator of terms a, b = 1, 3 while True: yield from (a,)*(b-a) a, b = b, a+b A352717_list = list(islice(A352717_gen(),40)) # Chai Wah Wu, Jun 08 2022
a(1) = (0 + 2 - 2*1) = 0; a(2) = (0 + 2 - 2*1) + (1 + 3 - 2*2) = 0; a(3) = (0 + 2 - 2*1) + (1 + 3 - 2*2) + (2 + 5 - 2*3) = 1; a(4) = (0 + 2 - 2*1) + (1 + 3 - 2*2) + (2 + 5 - 2*3) + (3 + 5 - 2*4) = 1.
isfib(k) = my(m=5*k^2); issquare(m-4) || issquare(m+4); nextfib(n) = my(k=n+1); while (!isfib(k), k++); k; prevfib(n) = my(k=n-1); while (!isfib(k), k--); k; a(n) = sum(k=1, n, prevfib(k) + nextfib(k) - 2*k); \\ Michel Marcus, Apr 10 2020
Accumulate[Flatten[Map[ConstantArray[LucasL[#],LucasL[#-1]]&,Range[15]]]] (* Peter J. C. Moses, May 02 2022 *)
from itertools import islice def A351628_gen(): # generator of terms a, b, c = 1, 3, 0 while True: yield from (c+i*a for i in range(1,b-a+1)) a, b, c = b, a+b, c + a*(b-a) A351628_list = list(islice(A351628_gen(),40)) # Chai Wah Wu, Jun 09 2022
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